Geodesic
Association and other forms of positive dependence for Feller evolution systems
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 369-391 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove characterizations of positive dependence for a general class of time-inhomogeneous Markov processes called Feller evolution processes (FEPs) and for jump-FEPs. General FEPs can be analyzed through their time and state-space dependent (extended) generators. We will use the time and state-space dependent (extended) generators and time and state-space dependent Lévy measures to characterize the positive dependence of general FEPs and jump-FEPs, respectively. We conclude with applications of these results to additive processes, which are time-inhomogeneous Lévy processes, often arising as useful examples in financial modeling.
Mots-clés : association
Keywords: orthant dependence, Feller evolutions system, additive process, time-inhomogeneous Markov process, comparison of Markov processes. 
@article{TVP_2021_66_2_a7,
     author = {E. Tu},
     title = {Association and other forms of positive dependence for {Feller} evolution systems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {369--391},
     year = {2021},
     volume = {66},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a7/}
}
TY  - JOUR
AU  - E. Tu
TI  - Association and other forms of positive dependence for Feller evolution systems
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 369
EP  - 391
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a7/
LA  - ru
ID  - TVP_2021_66_2_a7
ER  - 
%0 Journal Article
%A E. Tu
%T Association and other forms of positive dependence for Feller evolution systems
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 369-391
%V 66
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a7/
%G ru
%F TVP_2021_66_2_a7
E. Tu. Association and other forms of positive dependence for Feller evolution systems. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 369-391. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a7/

[1] B. Böttcher, “Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond”, PLoS ONE, 5:12 (2010), e15102, 8 pp. | DOI

[2] B. Böttcher, R. Schilling, Jian Wang, Lévy matters III. Lévy-type processes: construction, approximation and sample path properties, Lecture Notes in Math., 2099, Springer, Cham, 2013, xviii+199 pp. | DOI | MR | Zbl

[3] I. Herbst, L. Pitt, “Diffusion equation techniques in stochastic monotonicity and positive correlations”, Probab. Theory Related Fields, 87:3 (1991), 275–312 | DOI | MR | Zbl

[4] G. Samorodnitsky, “Association of infinitely divisible random vectors”, Stochastic Process. Appl., 55:1 (1995), 45–55 | DOI | MR | Zbl

[5] C. Houdré, V. Pérez-Abreu, D. Surgailis, “Interpolation, correlation identities, and inequalities for infinitely divisible variables”, J. Fourier Anal. Appl., 4:6 (1998), 651–668 | DOI | MR | Zbl

[6] N. Bäuerle, A. Blatter, A. Müller, “Dependence properties and comparison results for Lévy processes”, Math. Methods Oper. Res., 67:1 (2008), 161–186 | DOI | MR | Zbl

[7] T. M. Liggett, Interacting particle systems, Grundlehren Math. Wiss., 276, Springer-Verlag, New York, 1985, xv+488 pp. | DOI | MR | Zbl

[8] R. Szekli, Stochastic ordering and dependence in applied probability, Lect. Notes Stat., 97, Springer-Verlag, New York, 1995, viii+194 pp. | DOI | MR | Zbl

[9] L. Rüschendorf, “On a comparison result for Markov processes”, J. Appl. Probab., 45:1 (2008), 279–286 | DOI | MR | Zbl

[10] E. Tu, “On association and other forms of positive dependence for Feller processes”, J. Appl. Probab., 56:2 (2019), 624–646 | DOI | MR | Zbl

[11] B. Böttcher, “Feller evolution systems: generators and approximation”, Stoch. Dyn., 14:3 (2014), 1350025, 15 pp. | DOI | MR | Zbl

[12] L. Rüschendorf, A. Schnurr, V. Wolf, “Comparison of time-inhomogeneous Markov processes”, Adv. in Appl. Probab., 48:4 (2016), 1015–1044 | DOI | MR | Zbl

[13] E. B. Tu, Dependence structures in Lévy-type Markov processes, PhD diss., Univ. of Tennessee, Knoxville, 2017, ix+156 pp. https://trace.tennessee.edu/utk_graddiss/4661/

[14] A. Müller, D. Stoyan, Comparison methods for stochastic models and risks, Wiley Ser. Probab. Stat., John Wiley Sons, Ltd., Chichester, 2002, xii+330 pp. | MR | Zbl

[15] T. C. Christofides, E. Vaggelatou, “A connection between supermodular ordering and positive/negative association”, J. Multivariate Anal., 88:1 (2004), 138–151 | DOI | MR | Zbl

[16] D. Applebaum, Lévy processes and stochastic calculus, Cambridge Stud. Adv. Math., 93, Cambridge Univ. Press, Cambridge, 2004, xxiv+384 pp. | DOI | MR | Zbl

[17] P. Courrège, “Sur la forme intégro-différentielle des opérateurs de $C_k^\infty$ dans $C$ satisfaisant au principe du maximum”, Séminaire de Théorie du Potentiel, dirigé par M. Brelot, G. Choquet et J. Deny, 10 (1965–1966), no. 1, Secrétariat mathématique, Paris, 1967, Exposé no. 2, 38 pp. | MR | Zbl

[18] N. Jacob, Pseudo-differential operators and Markov processes, v. I, Fourier analysis and semigroups, Imperial College Press, London, 2001, xxii+493 pp. | DOI | MR | Zbl

[19] B. H. Lindqvist, “Monotone and associated Markov chains, with applications to reliability theory”, J. Appl. Probab., 24:3 (1987), 679–695 | DOI | MR | Zbl

[20] Mu-Fa Chen, Feng-Yu Wang, “On order-preservation and positive correlations for multidimensional diffusion processes”, Probab. Theory Related Fields, 95:3 (1993), 421–428 | DOI | MR | Zbl

[21] Jie Ming Wang, “Stochastic comparison and preservation of positive correlations for Lévy-type processes”, Acta Math. Sin. (Engl. Ser.), 25:5 (2009), 741–758 | DOI | MR | Zbl

[22] R. Cont, P. Tankov, Financial modelling with jump processes, Chapman Hall/CRC Financ. Math. Ser., Chapman Hall/CRC, Boca Raton, FL, 2004, xvi+535 pp. | DOI | MR | Zbl

[23] J. Jacod, A. N. Shiryaev, Limit theorems for stochastic processes, Grundlehren Math. Wiss., 288, 2nd ed., Springer-Verlag, Berlin, 2003, xx+661 pp. | DOI | MR | MR | MR | Zbl | Zbl

[24] K. Sato, Lévy processes and infinitely divisible distributions, Cambridge Stud. Adv. Math., 68, Cambridge Univ. Press, Cambridge, 1999, xii+486 pp. | MR | Zbl